Evaluate
68
Factor
2^{2}\times 17
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)1292}\\\end{array}
Use the 1^{st} digit 1 from dividend 1292
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)1292}\\\end{array}
Since 1 is less than 19, use the next digit 2 from dividend 1292 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)1292}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1292
\begin{array}{l}\phantom{19)}00\phantom{4}\\19\overline{)1292}\\\end{array}
Since 12 is less than 19, use the next digit 9 from dividend 1292 and add 0 to the quotient
\begin{array}{l}\phantom{19)}00\phantom{5}\\19\overline{)1292}\\\end{array}
Use the 3^{rd} digit 9 from dividend 1292
\begin{array}{l}\phantom{19)}006\phantom{6}\\19\overline{)1292}\\\phantom{19)}\underline{\phantom{}114\phantom{9}}\\\phantom{19)9}15\\\end{array}
Find closest multiple of 19 to 129. We see that 6 \times 19 = 114 is the nearest. Now subtract 114 from 129 to get reminder 15. Add 6 to quotient.
\begin{array}{l}\phantom{19)}006\phantom{7}\\19\overline{)1292}\\\phantom{19)}\underline{\phantom{}114\phantom{9}}\\\phantom{19)9}152\\\end{array}
Use the 4^{th} digit 2 from dividend 1292
\begin{array}{l}\phantom{19)}0068\phantom{8}\\19\overline{)1292}\\\phantom{19)}\underline{\phantom{}114\phantom{9}}\\\phantom{19)9}152\\\phantom{19)}\underline{\phantom{9}152\phantom{}}\\\phantom{19)9999}0\\\end{array}
Find closest multiple of 19 to 152. We see that 8 \times 19 = 152 is the nearest. Now subtract 152 from 152 to get reminder 0. Add 8 to quotient.
\text{Quotient: }68 \text{Reminder: }0
Since 0 is less than 19, stop the division. The reminder is 0. The topmost line 0068 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 68.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}